{
  "id": "1509.08026",
  "version": "v1",
  "published": "2015-09-26T21:00:11.000Z",
  "updated": "2015-09-26T21:00:11.000Z",
  "title": "Cell decompositions of quiver flag varieties for nilpotent representations of the oriented cycle",
  "authors": [
    "Julia Sauter"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Generalizing Schubert cells in type $A$ and a cell decomposition if Springer fibres in type $A$ found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation and describe the $T$-equivariant cohomology using Goresky-Kottwitz-MacPherson-theory. As an application of the cell decomposition we obtain a vector space basis of standard modules (for quiver Hecke algebras of nilpotent representations of this quiver) introduced by Kato.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-26T21:00:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "16G20"
    ],
    "keywords": [
      "nilpotent representations",
      "quiver flag varieties",
      "affine cell decomposition",
      "vector space basis",
      "quiver hecke algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150908026S"
    }
  }
}